Given a sorted positive integer array nums and an integer n, add/patch elements to the array such that any number in range [1, n] inclusive can be formed by the sum of some elements in the array. Return the minimum number of patches required.

Example 1: nums = [1, 3], n = 6 Return 1.

Combinations of nums are [1], [3], [1,3], which form possible sums of: 1, 3, 4. Now if we add/patch 2 to nums, the combinations are: [1], [2], [3], [1,3], [2,3], [1,2,3]. Possible sums are 1, 2, 3, 4, 5, 6, which now covers the range [1, 6]. So we only need 1 patch.

Example 2: nums = [1, 5, 10], n = 20 Return 2. The two patches can be [2, 4].

Example 3: nums = [1, 2, 2], n = 5 Return 0.

Solution

public class Solution {
    public int minPatches(int[] nums, int n) {
        long miss = 1;
        int ans = 0;
        int i = 0;
        while(miss <= n) {
            if(i < nums.length && miss >= nums[i]) {
                // use existing number
                miss += nums[i++];
            } else {
                // add a patch, the number "miss"
                miss += miss;
                ans++;
            }
        }
        return ans;
    }
}